PROBLEM 4 (20 points): Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and production cost (exclusive of raw materials) for each product are given in the table below. Currently, 900 labor hours, 1600 board feet of lumber and 1550 gallons of paint are available. Additional labor can be purchased at $6 per hour, additional paint at $2 per gallon, and additional lumber at $3 per board foot. Productco established the following goals: G1: Obtain a profit of at least 10500$ (any shortfall amount must be borrowed) G2: Purchase no additional labor G3: Purchase no additional lumber G4: Purchase no additional paint. Part A: Define the objective variables and write the constraints in mathematical format. PROBLEM 4 (20 points): Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and production cost (exclusive of raw materials) for each product are given in the table below. Currently, 900 labor hours, 1600 board feet of lumber and 1550 gallons of paint are available. Additional labor can be purchased at $6 per hour, additional paint at $2 per gallon, and additional lumber at $3 per board foot. Productco established the following goals: G1: Obtain a profit of at least 10500$ (any shortfall amount must be borrowed) G2: Purchase no additional labor G3: Purchase no additional lumber G4: Purchase no additional paint. Part A: Define the objective variables and write the constraints in mathematical format